Results for 'Douglas W. Bird'

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  1. (1 other version)Consequentializing.Douglas W. Portmore - forthcoming - Stanford Encyclopedia of Philosophy.
    This is an encyclopedia entry on consequentializing. It explains what consequentializing is, what makes it possible, why someone might be motivated to consequentialize, and how to consequentialize a non-consequentialist theory.
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  2. Desert, Control, and Moral Responsibility.Douglas W. Portmore - 2019 - Acta Analytica 34 (4):407-426.
    In this paper, I take it for granted both that there are two types of blameworthiness—accountability blameworthiness and attributability blameworthiness—and that avoidability is necessary only for the former. My task, then, is to explain why avoidability is necessary for accountability blameworthiness but not for attributability blameworthiness. I argue that what explains this is both the fact that these two types of blameworthiness make different sorts of reactive attitudes fitting and that only one of these two types of attitudes requires having (...)
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  3. A Comprehensive Account of Blame: Self-Blame, Non-Moral Blame, and Blame for the Non-Voluntary.Douglas W. Portmore - 2022 - In Andreas Brekke Carlsson (ed.), Self-Blame and Moral Responsibility. New York, USA: Cambridge University Press.
    Blame is multifarious. It can be passionate or dispassionate. It can be expressed or kept private. We blame both the living and the dead. And we blame ourselves as well as others. What’s more, we blame ourselves, not only for our moral failings, but also for our non-moral failings: for our aesthetic bad taste, gustatory self-indulgence, or poor athletic performance. And we blame ourselves both for things over which we exerted agential control (e.g., our voluntary acts) and for things over (...)
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  4. Transitivity, Moral Latitude, and Supererogation.Douglas W. Portmore - 2017 - Utilitas 29 (3):286-298.
    On what I take to be the standard account of supererogation, an act is supererogatory if and only if it is morally optional and there is more moral reason to perform it than to perform some permissible alternative. And, on this account, an agent has more moral reason to perform one act than to perform another if and only if she morally ought to prefer how things would be if she were to perform the one to how things would be (...)
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  5. Control, Attitudes, and Accountability.Douglas W. Portmore - 2013 - In David Shoemaker (ed.), Oxford studies in agency and responsibility. Oxford: Oxford University Press.
    It seems that we can be directly accountable for our reasons-responsive attitudes—e.g., our beliefs, desires, and intentions. Yet, we rarely, if ever, have volitional control over such attitudes, volitional control being the sort of control that we exert over our intentional actions. This presents a trilemma: (Horn 1) deny that we can be directly accountable for our reasons-responsive attitudes, (Horn 2) deny that φ’s being under our control is necessary for our being directly accountable for φ-ing, or (Horn 3) deny (...)
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  6.  52
    Review symposium : Douglas W. hands G. C. Archibald Joseph Agassi on S. J. Latsis, ed. method and appraisal in economics. Cambridge: Cambridge university press, 1976. Pp. VIII + 218. $17.50 the methodology of economic research programmes. [REVIEW]Douglas W. Hands - 1979 - Philosophy of the Social Sciences 9 (3):293-303.
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  7. Maximalism and Moral Harmony.Douglas W. Portmore - 2018 - Philosophy and Phenomenological Research (2):318-341.
    Maximalism is the view that an agent is permitted to perform a certain type of action if and only if she is permitted to perform some instance of this type, where φ-ing is an instance of ψ-ing if and only if φ-ing entails ψ-ing but not vice versa. Now, the aim of this paper is not to defend maximalism, but to defend a certain account of our options that when combined with maximalism results in a theory that accommodates the idea (...)
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  8. Consequentializing agent‐centered restrictions: A Kantsequentialist approach.Douglas W. Portmore - 2023 - Analytic Philosophy 64 (4):443-467.
    There is, on a given moral view, an agent-centered restriction against performing acts of a certain type if that view prohibits agents from performing an instance of that act-type even to prevent two or more others from each performing a morally comparable instance of that act-type. The fact that commonsense morality includes many such agent-centered restrictions has been seen by several philosophers as a decisive objection against consequentialism. Despite this, I argue that agent-centered restrictions are more plausibly accommodated within a (...)
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  9. Morality and Practical Reasons.Douglas W. Portmore - 2021 - Cambridge, United Kingdom: Cambridge University Press.
    As Socrates famously noted, there is no more important question than how we ought to live. The answer to this question depends on how the reasons that we have for living in various different ways combine and compete. To illustrate, suppose that I've just received a substantial raise. What should I do with the extra money? I have most moral reason to donate it to effective charities but most self-interested reason to spend it on luxuries for myself. So, whether I (...)
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  10. Moral Worth and Our Ultimate Moral Concerns.Douglas W. Portmore - forthcoming - Oxford Studies in Normative Ethics.
    Some right acts have what philosophers call moral worth. A right act has moral worth if and only if its agent deserves credit for having acted rightly in this instance. And I argue that an agent deserves credit for having acted rightly if and only if her act issues from an appropriate set of concerns, where the appropriateness of these concerns is a function what her ultimate moral concerns should be. Two important upshots of the resulting account of moral worth (...)
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  11. Deserving to Suffer.Douglas W. Portmore - forthcoming - The Journal of Ethics:1-19.
    I argue that the blameworthy deserve to suffer in that they deserve to feel guilt, which is the unpleasant experience of appreciating one’s apparent culpability for having done wrong. I argue that the blameworthy deserve to feel guilt because they owe it to those whom they’ve culpably wronged to (a) hold themselves accountable, (b) manifest the proper regard for those whom they’ve wronged, and (c) appreciate their culpability for, and the moral significance of, their wrongdoing. And I argue that the (...)
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  12. Morality, Rationality, and Performance Entailment.Douglas W. Portmore - manuscript
    The performance of one option can entail the performance of another. For instance, baking an apple pie entails baking a pie. Now, suppose that both of these options—baking a pie and baking an apple pie—are permissible. This raises the issue of which, if either, is more fundamental than the other. Is baking a pie permissible because it’s permissible to bake an apple pie? Or is baking an apple pie permissible because it’s permissible to bake a pie? Or are they equally (...)
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  13. What’s a rational self-torturer to do?Douglas W. Portmore - manuscript
    This paper concerns Warren Quinn’s famous “The Puzzle of the Self-Torturer.” I argue that even if we accept his assumption that practical rationality is purely instrumental such that what he ought to do is simply a function of how the relevant options compare to each other in terms of satisfying his actual preferences that doesn’t mean that every explanation as to why he shouldn’t advance to the next level must appeal to the idea that so advancing would be suboptimal in (...)
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  14. Consequentialism and Moral Rationalism.Douglas W. Portmore - 2011 - In Mark Timmons (ed.), Oxford Studies in Normative Ethics. New York: Oxford University Press.
    IN THIS PAPER, I make a presumptive case for moral rationalism: the view that agents can be morally required to do only what they have decisive reason to do, all things considered. And I argue that this view leads us to reject all traditional versions of act‐consequentialism. I begin by explaining how moral rationalism leads us to reject utilitarianism.
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  15. Acts, Attitudes, and Rational Choice.Douglas W. Portmore - manuscript
    In this paper, I argue that we have obligations not only to perform certain actions, but also to have certain attitudes (such as desires, beliefs, and intentions), and this despite the fact that we rarely, if ever, have direct voluntary control over our attitudes. Moreover, I argue that whatever obligations we have with respect to actions derive from our obligations with respect to attitudes. More specifically, I argue that an agent is obligated to perform an action if and only if (...)
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  16. Moral Worth Requires a Fundamental Concern for What Ultimately Matters.Douglas W. Portmore - manuscript
    An act that accords with duty has moral worth if and only if the agent’s reason for performing it is the same as what would have motivated a perfectly virtuous agent to perform it. On one of the two leading accounts of moral worth, an act that accords with duty has moral worth if and only if the agent’s reason for performing it is the fact that it’s obligatory. On the other, an act that accords with duty has moral worth (...)
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  17. Consequentialism and Coordination Problems.Douglas W. Portmore - manuscript
    Imagine both that (1) S1 is deliberating at t about whether or not to x at t' and that (2) although S1’s x-ing at t' would not itself have good consequences, good consequences would ensue if both S1 x's at t' and S2 y's at t", where S1 may or may not be identical to S2 and where t < t' ≤ t". In this paper, I consider how consequentialists should treat S2 and the possibility that S2 will y at (...)
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  18. Maximalism and Rational Control.Douglas W. Portmore - manuscript
    Maximalism is the view that if an agent is permitted to perform a certain type of action (say, baking), this is in virtue of the fact that she is permitted to perform some instance of this type (say, baking a pie), where φ-ing is an instance of ψ-ing if and only if φ-ing entails ψ-ing but not vice versa. Now, the point of this paper is not to defend maximalism, but to defend a certain account of our options that when (...)
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  19. Precis of Commonsense Consequentialism and Replies to Gert, Hurley, and Tenenbaum.Douglas W. Portmore - forthcoming - Philosophy and Phenomenological Research.
    For a symposium on Douglas W. Portmore's Commonsense Consequentialism: Wherein Morality Meets Rationality.
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  20. Acts, Attitudes, and Rational Control.Douglas W. Portmore - manuscript
    I argue that when determining whether an agent ought to perform an act, we should not hold fixed the fact that she’s going to form certain attitudes (and, here, I’m concerned with only reasons-responsive attitudes such as beliefs, desires, and intentions). For, as I argue, agents have, in the relevant sense, just as much control over which attitudes they form as which acts they perform. This is important because what effect an act will have on the world depends not only (...)
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  21. Parfit on Reasons and Rule Consequentialism.Douglas W. Portmore - 1998 - In Martina Herrmann (ed.), Reading Parfit. Springer Netherlands.
    I argue that rule consequentialism sometimes requires us to act in ways that we lack sufficient reason to act. And this presents a dilemma for Parfit. Either Parfit should concede that we should reject rule consequentialism (and, hence, Triple Theory, which implies it) despite the putatively strong reasons that he believes we have for accepting the view or he should deny that morality has the importance he attributes to it. For if morality is such that we sometimes have decisive reason (...)
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  22. Foundational Consequentialism and Its Primary Evaluative Focal Point.Douglas W. Portmore - manuscript
    Following Shelly Kagan’s useful terminology, foundational consequentialists are those who hold that the ranking of outcomes is at the foundation of all moral assessment. That is, they hold that moral assessments of right and wrong, virtuous and vicious, morally good and morally bad, etc. are all ultimately a function of how outcomes rank. But foundational consequentialists disagree on what is to be directly evaluated in terms of the ranking of outcomes, which is to say that they disagree on what the (...)
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  23. Review of Martin Peterson's The Dimensions of Consequentialism. [REVIEW]Douglas W. Portmore - forthcoming - Journal of Moral Philosophy.
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  24. Analogical Reasoning and Semantic Rules of Inference.Fabrizio Macagno, Douglas Walton & Christopher W. Tindale - 2014 - Revue Internationale de Philosophie 270 (4):419-432.
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  25. Thinking in transition: Nishida Kitaro and Martin Heidegger.Elmar Weinmayr, tr Krummel, John W. M. & Douglas Ltr Berger - 2005 - Philosophy East and West 55 (2):232-256.
    : Two major philosophers of the twentieth century, the German existential phenomenologist Martin Heidegger and the seminal Japanese Kyoto School philosopher Nishida Kitarō are examined here in an attempt to discern to what extent their ideas may converge. Both are viewed as expressing, each through the lens of his own tradition, a world in transition with the rise of modernity in the West and its subsequent globalization. The popularity of Heidegger's thought among Japanese philosophers, despite its own admitted limitation to (...)
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  26. Percy W. Bridgman e a análise do Operacionalismo em 1953 (3rd edition).Douglas Antonio Bassani - 2023 - Pensando - Revista de Filosofia 14:33-43.
    Este artigo procura analisar algumas das principais ideias abordadas no encontro anual promovido pela “American Association for the Advancement of Sciencie” em Boston (EUA) em 1953. Parte do encontro foi para abordar sobre o estado atual da concepção operacional de significado desenvolvida por Percy W. Bridgman a partir de 1927. As principais ideias tratadas no encontro foram posteriormente publicadas pela revista “The Scientific Montly” em 1954-1955 e republicadas no capítulo 2 do livro “The validation of scientific theories” (1961), editado por (...)
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  27. Bird on Kant's Mathematical Antinomies.A. W. Moore - 2011 - Kantian Review 16 (2):235-243.
    This essay is concerned with Graham Bird’s treatment, in The Revolutionary Kant, of Kant’s mathematical antinomies. On Bird’s interpretation, our error in these antinomies is to think that we can settle certain issues about the limits of physical reality by pure reason whereas in fact we cannot settle them at all. On the rival interpretation advocated in this essay, it is not true that we cannot settle these issues. Our error is to presuppose that the concept of the (...)
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  28. (1 other version)Second thoughts: A reply to mr Ginnane's thoughts.Douglas C. Long - 1961 - Mind 70 (July):405-411.
    In his article "Thoughts" (MIND, July 1960) William Ginnane argues that "thought is pure intentionality," and that our thoughts are not embodied essentially in the mental imagery and other elements of phenomenology that cross our minds along with the thoughts. Such images merely illustrate out thoughts. In my discussion I resist this claim pointing out that our thoughts are often embodied in events that can be described in phenomenological terms, especially when our reports of our thinking are introduced by the (...)
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  29. Teaching Philosophy through Lincoln-Douglas Debate.Jacob Nebel, Ryan W. Davis, Peter van Elswyk & Ben Holguin - 2013 - Teaching Philosophy 36 (3):271-289.
    This paper is about teaching philosophy to high school students through Lincoln-Douglas (LD) debate. LD, also known as “values debate,” includes topics from ethics and political philosophy. Thousands of high school students across the U.S. debate these topics in class, after school, and at weekend tournaments. We argue that LD is a particularly effective tool for teaching philosophy, but also that LD today falls short of its potential. We argue that the problems with LD are not inevitable, and we (...)
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  30. Gloomy duck or cheerful rabbit?Christine Tappolet & Bruce Maxwell - 2012 - Philosophy, Psychiatry, and Psychology 19 (1):21-23.
    Reply to Ronald de Sousa and Douglas W. Heinrichs.
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  31. A concept of progress for normative economics.Philippe Mongin - 2006 - Economics and Philosophy 22 (1):19-54.
    The paper discusses the sense in which the changes undergone by normative economics in the twentieth century can be said to be progressive. A simple criterion is proposed to decide whether a sequence of normative theories is progressive. This criterion is put to use on the historical transition from the new welfare economics to social choice theory. The paper reconstructs this classic case, and eventually concludes that the latter theory was progressive compared with the former. It also briefly comments on (...)
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  32.  61
    Is Long-Term Thinking a Trap?: Chronowashing, Temporal Narcissism, and the Time Machines of Racism.Michelle Bastian - 2024 - Environmental Humanities 16 (2):403–421.
    This provocation critiques the notion of long-term thinking and the claims of its proponents that it will help address failures in dominant conceptions of time, particularly in regard to environmental crises. Drawing on analyses of the Clock of the Long Now and Kim Stanley Robinson’s The Ministry for the Future, the article suggests that we be more wary of the concept’s use in what we might call chronowashing. Like the more familiar greenwashing, where environmental issues are hidden by claims to (...)
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  33. Aristotle on the Relations between Genera, Species and Differentia.Mohammad Bagher Ghomi - manuscript
    The following are the characteristics of a genus: 1. Those to which the same figure of predication applies are one in genus. (Met. , Δ, 1016b32-35) 2. Things that are one in genus are all one by analogy while things that are one by analogy are not all one in genus. (Met, Δ, 1016b35-1017a3) 3. A genus includes contraries. (Met., Δ, 1018a25-31) 4. All the intermediates are in the same genus as one another and as the things they stand between. (...)
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  34. A search for new physics in high-mass ditau events in the ATLAS detector.Ryan Reece - 2013 - Dissertation, University of Pennsylvania
    This thesis is a work of experimental physics, a search for new physics with the ATLAS experiment. I post this thesis on the PhilArchive because it includes a pedagogical summary of quantum mechanics and the standard model of particle physics in the combination of chapters 1-2 and appendix A. This was my attempt at the end of my PhD of giving a bird's eye view of the standard model, with a thorough bibliography of the publication trail that lead to (...)
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  35. Online Deliberation: Design, Research, and Practice.Todd Davies & Seeta Peña Gangadharan (eds.) - 2009 - CSLI Publications/University of Chicago Press.
    Can new technology enhance purpose-driven, democratic dialogue in groups, governments, and societies? Online Deliberation: Design, Research, and Practice is the first book that attempts to sample the full range of work on online deliberation, forging new connections between academic research, technology designers, and practitioners. Since some of the most exciting innovations have occurred outside of traditional institutions, and those involved have often worked in relative isolation from each other, work in this growing field has often failed to reflect the full (...)
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  36. Computing and philosophy: Selected papers from IACAP 2014.Vincent C. Müller (ed.) - 2016 - Cham: Springer.
    This volume offers very selected papers from the 2014 conference of the “International Association for Computing and Philosophy” (IACAP) - a conference tradition of 28 years. - - - Table of Contents - 0 Vincent C. Müller: - Editorial - 1) Philosophy of computing - 1 Çem Bozsahin: - What is a computational constraint? - 2 Joe Dewhurst: - Computing Mechanisms and Autopoietic Systems - 3 Vincenzo Fano, Pierluigi Graziani, Roberto Macrelli and Gino Tarozzi: - Are Gandy Machines really local? (...)
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  37. Psychological Operationisms at Harvard: Skinner, Boring, and Stevens.Sander Verhaegh - 2021 - Journal of the History of the Behavioral Sciences 57 (2):194-212.
    Contemporary discussions about operational definition often hark back to Stanley Smith Stevens’ classic papers on psychological operationism (1935ab). Still, he was far from the only psychologist to call for conceptual hygiene. Some of Stevens’ direct colleagues at Harvard---most notably B. F. Skinner and E. G. Boring---were also actively applying Bridgman’s conceptual strictures to the study of mind and behavior. In this paper, I shed new light on the history of operationism by reconstructing the Harvard debates about operational definition in the (...)
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  38. Wittgenstein Didn’t Agree with Gödel - A.P. Bird - Cantor’s Paradise.A. P. Bird - 2021 - Cantor's Paradise (00):00.
    In 1956, a few writings of Wittgenstein that he didn't publish in his lifetime were revealed to the public. These writings were gathered in the book Remarks on the Foundations of Mathematics (1956). There, we can see that Wittgenstein had some discontentment with the way philosophers, logicians, and mathematicians were thinking about paradoxes, and he even registered a few polemic reasons to not accept Gödel’s incompleteness theorems.
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  39. An arugmentation framework for contested cases of statutory interpertation.Douglas Walton, Giovanni Sartor & Fabrizio Macagno - 2016 - Artificial Intelligence and Law 24 (1):51-91.
    This paper proposes an argumentation-based procedure for legal interpretation, by reinterpreting the traditional canons of textual interpretation in terms of argumentation schemes, which are then classified, formalized, and represented through argument visualization and evaluation tools. The problem of statutory interpretation is framed as one of weighing contested interpretations as pro and con arguments. The paper builds an interpretation procedure by formulating a set of argumentation schemes that can be used to comparatively evaluate the types of arguments used in cases of (...)
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  40. Neural and Environmental Modulation of Motivation: What's the Moral Difference?Thomas Douglas - 2018 - In David Birks & Thomas Douglas (eds.), Treatment for Crime: Philosophical Essays on Neurointerventions in Criminal Justice. Oxford: Oxford University Press.
    Interventions that modify a person’s motivations through chemically or physically influencing the brain seem morally objectionable, at least when they are performed nonconsensually. This chapter raises a puzzle for attempts to explain their objectionability. It first seeks to show that the objectionability of such interventions must be explained at least in part by reference to the sort of mental interference that they involve. It then argues that it is difficult to furnish an explanation of this sort. The difficulty is that (...)
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  41. A Policy of No Interest? The Permanent Zero Interest Rate, and the Evils of Capitalism.Alexander Douglas - manuscript
    In 1937 Joan Robinson proposed that “when capitalism is rightly understood, the rate of interest will be set at zero and the major evils of capitalism will disappear”. A permanent zero rate would abolish capitalist profit except in limited cases, leaving nearly all output to be claimed by labour as wages. It would allow capital to be allocated on the basis of prospective social benefit rather than short-term profitability and a collateral basis that favours the wealthy. It would remove some (...)
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  42. Public Policy Experiments without Equipoise: When is Randomization Fair?Douglas MacKay & Emma Cohn - 2023 - Ethics and Human Research 45 (1):15-28.
    Government agencies and nonprofit organizations have increasingly turned to randomized controlled trials (RCTs) to evaluate public policy interventions. Random assignment is widely understood to be fair when there is equipoise; however, some scholars and practitioners argue that random assignment is also permissible when an intervention is reasonably expected to be superior to other trial arms. For example, some argue that random assignment to such an intervention is fair when the intervention is scarce, for it is sometimes fair to use a (...)
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  43. Plato on Sunaitia.Douglas R. Campbell - 2023 - Apeiron 56 (4):739-768.
    I argue that Plato thinks that a sunaition is a mere tool used by a soul (or by the cosmic nous) to promote an intended outcome. In the first section, I develop the connection between sunaitia and Plato’s teleology. In the second section, I argue that sunaitia belong to Plato’s theory of the soul as a self-mover: specifically, they are those things that are set in motion by the soul in the service of some goal. I also argue against several (...)
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  44. The Soul’s Tomb: Plato on the Body as the Cause of Psychic Disorders.Douglas R. Campbell - 2022 - Apeiron 55 (1):119-139.
    I argue that, according to Plato, the body is the sole cause of psychic disorders. This view is expressed at Timaeus 86b in an ambiguous sentence that has been widely misunderstood by translators and commentators. The goal of this article is to offer a new understanding of Plato’s text and view. In the first section, I argue that although the body is the result of the gods’ best efforts, their sub-optimal materials meant that the soul is constantly vulnerable to the (...)
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  45. Análise da interpretação possível do geocentrismo através das tradições de pesquisa.Douglas Antonio Bassani - 2023 - Griot : Revista de Filosofia 23:59-69.
    A pesquisa tem como objetivo analisar aspectos/elementos da cosmologia de Aristóteles a partir da filosofia da ciência de Larry Laudan. A tentativa é apresentar neste artigo uma interpretação possível sobre o processo evolutivo da cosmologia da época sob o enfoque da filosofia de Laudan, baseado nas tradições de pesquisa, teorias específicas, modelo reticulado, progresso científico, metodologia, axiologia, etc. Abordaremos sobre a questão da aceitação das teorias específicas, a questão da eficácia na resolução de problemas, entre outras questões importantes para a (...)
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  46. An Expected Value Approach to the Dual-Use Problem.Thomas Douglas - 2013 - In Selgelid Michael & Rappert Brian (eds.), On the Dual Uses of Science and Ethics. Australian National University Press.
    In this chapter I examine how expected-value theory might inform responses to what I call the dual-use problem. I begin by defining that problem. I then outline a procedure, which invokes expected-value theory, for tackling it. I first illustrate the procedure with the aid of a simplified schematic example of a dual-use problem, and then describe how it might also guide responses to more complex real-world cases. I outline some attractive features of the procedure. Finally, I consider whether and how (...)
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  47. Chapter 2 Identifying Policy Problems.Douglas MacKay - manuscript
    Policy analyses begin with a systematic overview of the policy problem they address. This includes a comprehensive discussion of the nature and context of the problem, and the institutional and behavioral factors responsible for its emergence. Problem statements must also explain why the status quo is bad or undesirable, why it is something that governments, rather than private actors, should address, and establish that the relevant government institutions have the legitimacy to intervene. In this chapter, I provide an overview of (...)
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  48. Designing a just soda tax.Douglas MacKay & Alexandria Huber-Disla - 2024 - Economics and Philosophy 40 (2):353-373.
    Soda taxes are controversial. While proponents point to their potential health benefits and the public projects that could be funded with their revenue, critics argue that they are paternalistic and regressive. In this paper, we explore the prospects for designing a just soda tax, one that appropriately balances the often-competing ethical considerations of promoting social welfare, respecting people’s autonomy and ensuring distributive fairness. We argue that policymakers have several paths forward for designing a just soda tax, but that the considerations (...)
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  49. Against Lewis on ‘Desire as Belief’.Douglas Ian Campbell - 2017 - Polish Journal of Philosophy 11 (1):17-28.
    David Lewis describes, then attempts to refute, a simple anti-Humean theory of desire he calls ‘Desire as Belief’. Lewis’ critics generally accept that his argument is sound and focus instead on trying to show that its implications are less severe than appearances suggest. In this paper I argue that Lewis’ argument is unsound. I show that it rests on an essential assumption that can be straightforwardly proven false using ideas and principles to which Lewis is himself committed.
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  50. Logicism, Formalism, and Intuitionism.A. P. Bird - 2021 - Cantor's Paradise (00):00.
    This paper objectively defines the three main contemporary philosophies of mathematics: formalism, logicism, and intuitionism. Being the three leading scientists of each: Hilbert (formalist), Frege (logicist), and Poincaré (intuitionist).
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